A291022 Even numbers m such that every odd divisor > 1 of m is the sum of two divisors.

6, 12, 18, 20, 24, 30, 36, 40, 42, 48, 54, 80, 96, 100, 108, 140, 150, 156, 160, 162, 192, 198, 200, 220, 264, 272, 280, 294, 312, 320, 324, 342, 384, 396, 400, 440, 486, 500, 510, 520, 528, 544, 546, 560, 624, 640, 684, 702, 714, 750, 768, 798, 800, 880, 912

Offset: 1

Author

Michel Lagneau, Aug 31 2017

Keywords

• nonn

Comments

The numbers of the form p*2^q (6, 12, 20, ...) where p belongs to the set {3, 5, 17, 257, 65537} (A019434: Fermat primes or primes of the form 2^(2^k) + 1, for some k >= 0) are in the sequence.

The sequence is included in A088723 (Numbers having at least one divisor d>1 such that also d+1 is a divisor).

Examples

			42 is in the sequence because the divisors are {1, 2, 3, 6, 7, 14, 21, 42} and 3 = 2 + 1, 7 = 6 + 1 and 21 = 14 + 7.
		

Crossrefs

Cf. A019434, A088723.

Programs

Maple

with(numtheory):EV:=array(1..100):OD:=array(1..100):nn:=5*10^4:
for n from 2 by 2 to nn do:
  d:=divisors(n):n1:=nops(d):k0:=0:k1:=0:it:=0:
   for i from 1 to n1 do:
    if irem(d[i],2)=0
     then
     k0:=k0+1:EV[k0]:=d[i]:
     else
     k1:=k1+1:OD[k1]:=d[i]:
    fi:
   od:
     for j from 2 to k1 do:
       for k from 1 to k1 do:
         for l from 1 to k0 do:
          if OD[j]=OD[k]+EV[l]
         then
          it:=it+1:
          else
         fi:
       od:
      od:
     od:
     if it>0 and it = k1-1
      then
      printf(`%d, `,n):
      else
     fi:
  od: